https://file.aiquickdraw.com/mathbot/file/1730458981584341c16s4.jpg

It appears that this is a multiplication table, and the objective is likely to fill in the missing cells by calculating products based on given numbers in the grid. 

Here's how I would approach this:

1. Determine the values that should be on the rows and columns.
2. Multiply each row header by each column header and fill in the appropriate cells.

Let me zoom in on the image to extract the data. I'll clarify the steps further.The table contains a multiplication grid with certain row and column headers provided:

- Top row headers: blank, 6, -9, and 4.
- Left column headers: -7, 10, and -8.

Here’s how we calculate the missing values by multiplying each row header with each column header:

### Step-by-Step Multiplication
1. **Row -7:**
   - \(-7 \times 6 = -42\)
   - \(-7 \times -9 = 63\)
   - \(-7 \times 4 = -28\)

2. **Row 10:**
   - \(10 \times 6 = 60\)
   - \(10 \times -9 = -90\)
   - \(10 \times 4 = 40\)

3. **Row -8:**
   - \(-8 \times 6 = -48\)
   - \(-8 \times -9 = 72\)
   - \(-8 \times 4 = -32\)

### Filled Table
Here's the completed multiplication table:

|      | 6   | -9  | 4   |
|------|-----|-----|-----|
| -7   | -42 | 63  | -28 |
| 10   | 60  | -90 | 40  |
| -8   | -48 | 72  | -32 |

Would you like more details on any specific calculations?

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### Additional Questions for Exploration
1. What are the effects of negative numbers on multiplication in a grid format?
2. How would this table look if all values were positive?
3. What if we replaced multiplication with addition in this table?
4. How can such tables help in learning multiplication with negative numbers?
5. How do different row and column values affect the range of products?

### Tip
In multiplication, remember that a positive times a negative gives a negative result, while a negative times a negative gives a positive.

Fill in the missing values in a multiplication table with given numbers in the rows and columns.

Learn how to fill in a multiplication table by calculating the products of integers, including negative and positive numbers. This exercise enhances understanding of integer arithmetic and the properties of multiplication. Suitable for Grades 6-8.

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